Okay, here we have this:
Considering the provided information we are going to replace in the formula of continuous compound interest:
[tex]\begin{gathered} A=Pe^{rt} \\ 3500=Pe^{(0.065\cdot4)} \end{gathered}[/tex]Now, let's solve for P:
[tex]\begin{gathered} P=\frac{3500}{e^{0.26}} \\ P=$2,698.68$ \end{gathered}[/tex]Finally we obtain that should be invested $2,698.68.
Find the principal P that corresponds to the future value F= $1,300 under r = 4% interest compounded daily for t = 3 years. Round your final answer to two decimal places.
The formula to find the principal is:
[tex]FV=P(1+i)^n[/tex]Where
FV is future value
P is principal
i is the rate of interest
n is the time frame
Given,
FV = 1300
i = r = 4%, or 4/100 = 0.04
n = t = 3
Plugging into formula and solving gives us:
[tex]\begin{gathered} FV=P(1+i)^n \\ 1300=P(1+0.04)^3 \\ 1300=P(1.04)^3 \\ P=\frac{1300}{1.04^3} \\ P=1155.695 \end{gathered}[/tex]Rounding to 2 decimal places:
$1155.70
The total cost of a jacket and shirt was $75.08 if the price of the jacket was $5.32 less than the shirt what was the price of the jacket
Let 'j' be the cost of the jacket and let 's' be the cost of the shirt. Then, if they cost $75.08, then we have the following expression:
[tex]j+s=75.08[/tex]since the price of the jacket was 5.32 less than the shirt, then, we have:
[tex]j=s-5.32[/tex]using this equation on the first equation, we get the following:
[tex]\begin{gathered} s-5.32+s=75.08 \\ \Rightarrow2s=75.08+5.32=80.40 \\ \Rightarrow s=\frac{80.40}{2}=40.20\rbrack \\ s=40.20 \end{gathered}[/tex]now that we have that the shirt costs $40.20, we can find the price of the jacket:]
[tex]j=40.20-5.32=34.88[/tex]therefore, the price of the jacket is $34.88 and the price of the shirt costs $40.20
I need help with my math
Given the question
4 (3x -6) + 2x + 18
To simplify the above expression, we will observe the following steps
Step 1: Expand the parenthesis (bracket)
[tex]\begin{gathered} 4(3x-6)+2x+18 \\ \Rightarrow4\times3x-\text{ 4x6 + 2x+18} \\ \Rightarrow12x\text{ -24+2x +18} \end{gathered}[/tex]Step 2: Simplify the expression by collecting like terms
[tex]\Rightarrow\text{ 12x +2x -24+18}[/tex][tex]14x\text{ -6}[/tex]Answer = 14x - 6
Latex paint sales for $25 per gallon and will cost you $175 to paint your room if each gallon will cover 330 ft.² how many square feet of wall space do you have in your room
The square feet of wall space in your room if paint cost $25 per gallon and will cost you $175 to paint the room is 2,310 square feet
What is the square feet of wall space in your room?Cost of latex paint per gallon = $25Total cost of paint = $175Square feet covered by each gallon = 330 ft.²Number of latex paint need to paint your room = Total cost of paint / Cost of latex paint per gallon
= $175 / $25
= 7 gallons
Number of square feet of wall space in your room = Number of latex paint need to paint your room × Square feet covered by each gallon
= 7 × 330
= 2,310 square feet
In conclusion, the square feet of wall space in your room is 2,310 square feet
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Stats, Practice Test 5-6 ) There is a class with 6 women and 12 men. a) If I randomly pick 5 students, with replacement. What is the probability that at least 4 of them will be man? b) If I randomly pick 6 students, what is the probability that at least one of them will be a man?
Step 1: Problem
There is a class with 6 women and 12 men. a) If I randomly pick 5 students, with replacement. What is the probability that at least 4 of them will be man? b) If I randomly pick 6 students, what is the probability that at least one of them will be a man?
Step 2: Concept
Kyra is participating in a fundraiser walk-a-thon. She walks 3 miles in 45 minutes. If she continues to walk at the same rate, determine how many minutes it will take her to walk 7 miles. Show how you found your answer.
3 milles ---> 45 minutes
7 miles ---> x minutes
then
[tex]\begin{gathered} 3\times x=7\times45 \\ 3x=315 \\ \frac{3x}{3}=\frac{315}{3} \\ x=105 \end{gathered}[/tex]answer: 105 minutes for walk 7 miles
Sound is measured in decibels, using the formula d = 10 log() where P is the intensity of the sound and P, is the weakest sound the human ear can hear. A horn has a decibel warning of20. How many times more intense is this horn compared to the weakest sound heard to the human ear?
We have the following:
The formula is the following
[tex]d=10\log (\frac{P}{P_o})[/tex]From what the statement tells us, the value of d is equal to 20, now we replace and solving for P / Po
[tex]\begin{gathered} 10\log (\frac{P}{P_o})=20 \\ \frac{10}{10}\log (\frac{P}{P_o})=\frac{20}{10} \\ \log (\frac{P}{P_o})=2\rightarrow\log (x)=2\rightarrow x=10^2\rightarrow x=100 \\ \frac{P}{P_o}=100 \\ P=100\cdot P_o \end{gathered}[/tex]Therefore, the sound of the horn is about 100 more intense than the weakest sound heard to the human ear.
DreviousRandom numbers are useful forA creatingOB. beingOC. modelingOD. sellingReset Selectionreal-world situations that involve chance.
Given random numbers, it is important to remember that Random Numbers are defined as those numbers that each have the same probability of being selected.
In Statistics, random numbers are useful to model different real-world situations.
An example of random numbers is the numbers of a lottery.
Another example of random numbers is the numbers obtained by rolling a numbered dice.
Hence, the answer is: Option C.
the product of 8 and a number increased by 17
You have the following stament:
The product of 8 and a number increased by 17
In order to write the previous statment in an algebraic way, you take into account that "the product of 8 and a number" means the multiplication of 8 and a variable, which is "increased" by 17. That is, number 8 is multiplying the sum of a variable and 17.
Thus, you have:
The product of 8 and a number increased by 17:
8(x + 17)
at the rate shown in the table how many books were sold in 3 weeks
210 books were sold in 3 weeks
Explanation
Step 1
you can easily solve this by using a rule of three
number of weeks=1
sold books=70
then, the rate is
[tex]\text{rate}=\frac{70\text{ books}}{1\text{ we}ek}=70\text{ book}s\text{ per w}eek[/tex]Step 2
Let
x represents the number of books sold in 3 weeks,then the rate is
[tex]\text{rate}=\frac{x}{3\text{ w}eeks}[/tex]as the rates are equal
[tex]\begin{gathered} 70=\frac{x}{3} \\ Multiply\text{ both sides by 3} \\ 70\cdot3=\frac{x}{3}\cdot3 \\ x=210 \end{gathered}[/tex]I hope this helps you
Every week Ben collects a few pounds of paper to recycle. The graph below shows the total number of pounds of paper(y) that Ben collected in a certain amount of time (x), in weeks:
To obtain the amount of paper that would most likely be collected in 10 weeks, the following steps are necessary:
Step 1: Select two points that lie on the straight line and use the two points to derive the equation of the straight line, as follows:
Such two points could be: (x1, y1) = (0, 30) and (x2, y2) = (120, 3)
Using the following formula, we can derive the equation of the straight line:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Thus:
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow\frac{y-30_{}}{x-0_{}}=\frac{120_{}-30_{}}{3_{}-0_{}} \\ \Rightarrow\frac{y-30_{}}{x_{}}=\frac{90_{}}{3_{}_{}} \\ \Rightarrow\frac{y-30_{}}{x_{}}=30 \\ \Rightarrow y-30=30\times x \\ \Rightarrow y=30x+30 \end{gathered}[/tex]The above equation can be re-written as:
[tex]\begin{gathered} y=30x+30 \\ \Rightarrow\text{Amount of paper collected = 30 }\times number\text{ of w}eeks\text{ + 30 } \end{gathered}[/tex]Step 2: Use the derived equation to obtain the value of the amount of paper collected in 10 weeks, as follows:
In 10 weeks, we will have :
[tex]\begin{gathered} \text{Amount of paper collected = 30 }\times number\text{ of w}eeks\text{ + 30 } \\ \Rightarrow\text{Amount of paper collected = 30 }\times10\text{ + 30 } \\ \Rightarrow\text{Amount of paper collected = 300 + 30 }=330 \\ \Rightarrow\text{Amount of paper collected = 3}30 \end{gathered}[/tex]Therefore, the amount of paper that would most likely be collected in 10 weeks is 330
Consider the following function.f(x) = |x − 9|Find the derivative from the left at x = 9. If it does not exist, enter NONE.Find the derivative from the right at x = 9. If it does not exist, enter NONE.
The form of the derivative of the absolute equation is
[tex]\begin{gathered} f(x)=\lvert x-a\rvert \\ \frac{dx}{dy}=\frac{\lvert x-a\rvert}{x-a} \\ \frac{dy}{dx}=\frac{x-a}{\lvert x-a\rvert} \end{gathered}[/tex]For the given function
[tex]f(x)=\lvert x-9\rvert[/tex]We will find the derivative from the left at x = 9
[tex]\frac{dy}{dx}=\frac{x-9}{\lvert x-9\rvert}[/tex]Substitute x by 9
[tex]\begin{gathered} \frac{dy}{dx}=\frac{9-9}{\lvert9-9\rvert} \\ \frac{dy}{dx}=\frac{0}{0} \end{gathered}[/tex]Then dy/dx does not exist (None)
The derivative from right at x = 9
[tex]\frac{dx}{dy}=\frac{\lvert x-9\rvert}{x-9}[/tex]Substitute x by 9
[tex]\begin{gathered} \frac{dx}{dy}=\frac{\lvert9-9\rvert}{9-9} \\ \frac{dx}{dy}=\frac{0}{0} \end{gathered}[/tex]Then dx/dy does not exist (None)
The Rainforest Pyramid at Moody Gardens is a rectangular pyramid that has glass sides to allow the sunlight to enter the building. The base of the building is approximately 320 feet wide and 200 feet long. The height of each side is approximately 140 feet. How many square feet of glass were needed to cover the lateral sides of the pyramid?
We have the following diagram for a rectangular pyramid:
Where:
• h is the height of the pyramid,
,• s is the slant height, the height of the sides.
The area of the sides (without the base) of the pyramid is given by:
[tex]A=\frac{1}{2}\cdot p\cdot s\text{.}[/tex]Where p is the perimeter of the base.
We have a rectangular pyramid with:
• base with sides a = 320 ft and b = 200 ft,
,• slant height (heigh of the sides ) s = 140 ft.
The perimeter of the base is:
[tex]p=2\cdot(a+b)=2\cdot(320ft+200ft)=1040ft\text{.}[/tex]Replacing the value of p and s in the formula of the area we get:
[tex]A=\frac{1}{2}\cdot(1040ft)\cdot140ft=72800ft^2.[/tex]Answer
It was needed 72800 ft² of glass.
Consider the equation 14 x 10^0.5w= 100.Solve the equation for w. Express the solution as a logarithm in base-10.W = _____ Approximate the value of w. Round your answer to the nearest thousandth.w ≈ _____
Solution:
Given;
[tex]14\cdot10^{0.5w}=100[/tex]Divide both sides by 14, we have;
[tex]\begin{gathered} \frac{14\cdot10^{0.5w}}{14}=\frac{100}{14} \\ \\ 10^{0.5w}=\frac{50}{7} \end{gathered}[/tex]Take the logarithm of both sides; we have;
[tex]\log_{10}(10)^{0.5w}=\log_{10}(\frac{50}{7})[/tex]Applying logarithmic laws;
[tex]0.5w=\log_{10}(\frac{50}{7})[/tex]Divide both sides by 0.5;
[tex]\begin{gathered} \frac{0.5w}{0.5}=\frac{\log_{10}(\frac{50}{7})}{0.5} \\ \\ w=\frac{\operatorname{\log}_{10}(\frac{50}{7})}{0.5} \end{gathered}[/tex](b)
[tex]\begin{gathered} w=\frac{\operatorname{\log}_{10}(\frac{50}{7})}{0.5} \\ \\ w\approx1.708 \end{gathered}[/tex]During a hurricane evacuation from the east coast of Georgia, a family traveled 200 miles west. For part of the trip, they averaged 60 mph, but as the congestion got bad, they had to slow to 10 mph. If the total time ct travel was 6 hours, how many miles did they drive at the reduced speed?
Given:
Total distanced traveled is 200 miles.
speed is 60 mph, but as the congestion got bad, they had to slow to 10 mph.
Time = 6 hours.
Let, x be the travel time at 60 mph
The equation is,
[tex]\begin{gathered} 60x+10(6-x)=200 \\ 60x+60-10x=200 \\ 50x=200-60 \\ 50x=140 \\ x=\frac{140}{50} \\ x=2.8 \end{gathered}[/tex]It mean at the speed of 60 mph, the distance traveled is,
[tex]60x=60(2.8)=168\text{ miles}[/tex]So, the distance traveled for the speed of 10 mph is,
[tex]200-168=32\text{ miles.}[/tex]Answer: The family traveled 32 miles at reduced speed.
m/cour16121/quizzes/2919544/take22A totem pole casts a shadow 45 feet long at the same time that a 6-foot-tallmancasts a shadow that is 3 feet long. Find the height of the totem pole.Height of the totemfeetHint: set a proportion like this oneshadow totemshadow manactual height totem actual height manucation
The totem pole with its shadow form a right triangle, and the same happens with the man and its shadow. Since it happens at the same time of the day, the "inclination" of the sunlight is the same for both, and those two triangles are similar, which means that their corresponding ratiso betweens sides are the same.
Using the hint given on the problem, we can estabilish the following equation for the height of the totem(let's call it h).
[tex]\frac{45}{h}=\frac{3}{6}[/tex]Now, we just need to solve for h.
[tex]\begin{gathered} \frac{45}{h}=\frac{3}{6} \\ \frac{45}{h}=\frac{1}{2} \\ \frac{h}{45}=2 \\ h=2\cdot45 \\ h=90 \end{gathered}[/tex]The height of the totem pole is 90 ft.
Pythagorean Theorem Task Card #1 A pool table is 9 feet long and 5 feet wide. How far is it from one corner pocket to the diagonally opposite corner pocket? Round to the nearest tenth.
A right triangle is made where the two legs are 9 ft (a) and 5 ft (b), and we have to find the hypotenuse (c). Using Pythagorean Theorem:
c² = a² + b²
c² = 9² + 5²
c² = 81 + 25
c = √106
c ≈ 10.3 ft
write an express to 4× + 12 by coming like terms
the initial expression is:
[tex]4x+12[/tex]We can see that they have in common a factor of 4 so we can rewrite it like:
[tex]4(x+3)[/tex]10. Linek is graphed below. Write an equation for line m that is perpendicular to line (there are multiple correct answers).
step 1
Find the equation of line k
the slope of line k is
m=-3/4 ------> previous answer
step 2
If two lines are perpendicular, then their slopes are opposite reciprocal
so
the slope of the line m must be equal to
m=4/3
I will assume a point (3,4)
Find the equation in slope intercept form
y=mx+b
we have
m=4/3
point (3,4)
substitute
4=(4/3)*(3)+b
solve for b
4=4+b
b=0
therefore
y=(4/3)x -----> equation in slope intercept form ( this line is perpendicular to line k)Find the equation in point slope form
y-y1=m(x-x1)
we have
m=4/3
point (3,4)
substitute
y-4=(4/3)*(x-3) -----> equation in point slope form ( this line is perpendicular to line k)Find the equation in standard form
Ax+By=C
where
A is a positive integer
B and C are integers
we have
y=(4/3)x
Multiply by 3 both sides
3y=4x
4x-3y=0 ------> equation in standard formy=(4/3)xy-4=(4/3)*(x-3)4x-3y=0What is the value of u? H 88 U +64 I K к 88 50 J U =
HK = KJ
So:
u+64 = 5u
Solve for u
Combine like terms:
64 = 5u-u
64= 4u
Divide both sides by 4
64/4 =4u/4
16 = u
two trains leave town 906 miles aprt at the same time and travel each other. one train travels 21 mi/h faster than other. if they meet in 6 hours, what is the rate of each train?
Let
x be the speed of the slower train
x + 21 be the speed of the faster train
They meet in 6 hours which means that their speed is
[tex]\frac{906}{6}=151[/tex]The sum of their therefore is
[tex]\begin{gathered} x+(x+21)=151 \\ 2x+21=151 \\ 2x=151-21 \\ 2x=130 \\ \frac{2x}{2}=\frac{130}{2} \\ x=65\frac{\operatorname{mi}}{\operatorname{h}}\text{ (speed of slower train)} \\ \\ x+21=65+21=86\frac{\operatorname{mi}}{\operatorname{h}}\text{ (speed of faster train)} \end{gathered}[/tex]Simply this expression 4(1-3x)+7x-8
Answer:
-5x-4
Step-by-step explanation:
4(1-3x)+7x-8
Distribute the 4
4(1)+4(-3x)+7x-8
4-12x+7x-8
Combine like terms
-12x+7x+4-8
-5x-4
hopes this helps please mark brainliest
Part BNow you’ll attempt to copy your original triangle using two of its angles:Choose two of the angles on ∆ABC, and locate the line segment between them. Draw a new line segment, DE¯, parallel to the line segment you located on ∆ABC. You can draw DE¯ of any length and place it anywhere on the coordinate plane, but not on top of ∆ABC.From points D and E, create an angle of the same size as the angles you chose on ∆ABC. Then draw a ray from D and a ray from E through the angles such that the rays intersect. You should now have two angles that are congruent to the angles you chose on ∆ABC.Label the point of intersection of the two rays F, and draw ∆DEF by creating a polygon through points D, E, and F.Take a screenshot of your results, save it, and insert the image in the space below.
Step 1)
We used angles alpha and betta from the original triangle
Step 2)
Then,
Step 3)
Notice that the two triangles are similar due to the AAA postulate. (The length of DE is different than that of AB)
The table gives a set of outcomes and their probabilities. Let A be the event "the outcom less than or equal to 2". Let B be the event "the outcome is a divisor of 3". Find P(AB). Outcome Probability 1 0.2 2 0.6 3 0.2
Given the table:
Outcome Probability
1 0.2
2 0.6
3 0.2
Let A be the event "the outcome less than or equal to 2.
Let B be the event "the outcome is a divisor of 3.
Let's find P(A ∩ B).
To find P(A ∩ B) let's first find P(A) and P(B).
Numbers less than or equal to 2 = 2 and 1
Outcomes less than or equal to 2 = P(2) or P(1)
Probability the outcome is less than or equal to 2 = P(A) = 0.2 + 0.6 = 0.8
Divisor of 3 = 1 and 3
Outcome is a divisor of 3 = P(1) and P(3)
Probability the outcome is a divisor of 3 = P(B) = 0.2 x 0.2 = 0.04
To find P(A ∩ B), we have:
P(A ∩ B) = P(A) x P(B) = 0.04 x 0.8 = 0.032
ANSWER:
0.032
The table lists recommended amounts of food to order for 25 party guests. Amanda and Syndey are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering purposes, they will count each of these "drop-in" guests as half a guest. How much of each food item should Amanda and Syndey order for a graduation party with 45 drop-in guests?
Amanda and Sydney are hosting a graduation party for 40 guests.
Also, they have 45 drop-in guests (each of these will count as half a guest).
Then, the total number of guests is:
[tex]40+\frac{45}{2}=\frac{40\times2+1\times45}{1\times2}=\frac{80+45}{2}=\frac{125}{2}[/tex]The table shows the recommended amounts of food for 25 party guests:
Fried Chicken: 24 pieces
Deli meats: 4 1/3 pounds
Lasagna: 10 3/4 pounds.
Let's find the proportion for 125/2 guests:
a. Fried chicken:
[tex]\begin{gathered} \frac{24\text{ pieces}}{25\text{ guests}}=\frac{x\text{ pieces}}{125/2\text{ guests}} \\ \text{Set the product of the diagonals equal to each other:} \\ 24\times\frac{125}{2}=x\times25 \\ \frac{24\times125}{2}=x\times25 \\ 1500=x\times25 \\ \text{Divide both sides by 25} \\ \frac{1500}{25}=\frac{x\times25}{25} \\ \text{Simplify} \\ 60=x \end{gathered}[/tex]Then, they'll need to order 60 units of fried chicken for the party.
b. Deli meats:
Start by converting the mixed number 4 1/3 into a fraction:
[tex]4\frac{1}{3}=\frac{4\times3+1}{3}=\frac{12+1}{3}=\frac{13}{3}[/tex]Now, apply proportions:
[tex]\begin{gathered} \frac{13/3\text{ pounds}}{25\text{ guests}}=\frac{x\text{ pounds}}{125/2\text{ guests}} \\ \text{Set the product of the diagonals equal to each other:} \\ x\times25=\frac{13}{3}\times\frac{125}{2} \\ x\times25=\frac{13\times125}{3\times2} \\ x\times25=\frac{1625}{6} \\ \text{Divide both sides by 25} \\ \frac{x\times25}{25}=\frac{1625}{6\times25}=\frac{1625}{150}=\frac{65}{6} \\ \text{Simplify} \\ x=\frac{65}{6} \end{gathered}[/tex]You also can convert this fraction into a mixed number:
[tex]\begin{gathered} \text{When you divide 65/6 you obtain a quotient of 10 and remainder 5.} \\ \text{Then the whole part is 10 and the fraction is 5/6} \\ \frac{65}{6}=10\frac{5}{6} \end{gathered}[/tex]Then, they'll need to order 10 5/6 pounds of deli meats for the party.
c. Lasagna
Convert the mixed number to fraction:
[tex]10\frac{3}{4}=\frac{10\times4+3}{4}=\frac{40+3}{4}=\frac{43}{4}[/tex]Apply proportions:
[tex]\begin{gathered} \frac{43/4\text{ pounds}}{25\text{ guests}}=\frac{x\text{ pounds}}{125/2\text{ guests}} \\ \text{Set the product of the diagonals equal to each other:} \\ x\times25=\frac{43}{4}\times\frac{125}{2} \\ x\times25=\frac{43\times125}{4\times2} \\ x\times25=\frac{5375}{8} \\ \text{Divide both sides by 25} \\ \frac{x\times25}{25}=\frac{5375}{8\times25}=\frac{5375}{200}=\frac{215}{8} \\ \text{Simplify} \\ x=\frac{215}{8} \end{gathered}[/tex]You also can convert this fraction into a mixed number:
[tex]\begin{gathered} \text{When you divide 215/8 you obtain a quotient of 26 and remainder 7.} \\ \text{Then the whole part is 26 and the fraction is 7/}8 \\ \frac{215}{8}=26\frac{7}{8} \end{gathered}[/tex]Then, they'll need to order 26 7/8 pounds of lasagna for the party.
Watch help videoFind the value of y in the diagram below.Y +9Y + 9Y +9y +9Y +9116Answer: Submit Answer
The equation from the box obtained is
[tex]y+9+y+9+y+9+y+9+y+9=116[/tex][tex]5y+45=116[/tex][tex]5y=71[/tex][tex]y=14.2[/tex]Parallelogram ABCD was translated to parallelogram AB'C'D'.How many units and in which direction were the x-coordinates of parallelogram ABCD moved?
Number of units: 7
Direction: left of the x coordinate
Explanation:Given:
Parallelogram ABCD was translated to parallelogram AB'C'D'
To find:
the number of units and in which direction were the x-coordinates of parallelogram ABCD moved
To determine the number of units, we will use the diagram below:
From A to A', B to B', C to C' and D to D', the number of units for the movement in the x coordinate is 7. The vertical position didn't change. This means to movement in the coordinate.
The parallelogram ABCD was moved to the left of the x axis to get parallelogram A'B'C'D'
Number of units: 7
Direction: left of the x coordinate
7 units to the left
Can’t figure this fraction equation. 5/6 is the fraction getting divided by 2. Answer must be in the simplest form
Solution:
5/6 divided by 2, i.e.
[tex]\frac{5}{6}\div2[/tex]Applying the fraction rule
[tex]\begin{gathered} \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c} \\ =\frac{5\times\:1}{6\times\:2} \\ =\frac{5}{6\times\:2} \\ =\frac{5}{12} \end{gathered}[/tex]Hence, the answer is 5/12
A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 4
percentage points with 95% confidence if
(a) he uses a previous estimate of 38%?
(b) he does not use any prior estimates?
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
(a) n =
(b) n=
(Round up to the nearest integer.)
(Round up to the nearest integer.)
The required sample sizes for the confidence intervals are given as follows:
a) Estimate of 38%: 566.
b) No estimate: 601.
How to obtain the required sample sizes?The margin of error for a confidence interval of proportions, using the z-distribution, is calculated as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The parameters of the equation are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The desired margin of error in this problem is of:
M = 0.04.
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For item a, the estimate is of [tex]\pi = 0.38[/tex], hence the sample size is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.38(0.62)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.38(0.62)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.38(0.62)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.38(0.62)}}{0.04}\right)^2[/tex]
n = 566.
For item b, when there is no estimate, we use [tex]\pi = 0.5[/tex], hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2[/tex]
n = 601.
More can be learned about the z-distribution at https://brainly.com/question/25890103
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ХI went to the bank 4 times last week and withdrew a total of $160. What was theaverage amount withdrew each time? Write and solve an expression to find theanswer